Low degree rational spline interpolation

For a strictly monotone function f on [a, b] we describe the possibility of finding an interpolating rational spline S of the form S(x) = c(0) + c(1)x/(1+d(1)x) on each subinterval of the grid a = x(0) < x(1) < ... < x(n) = b. This leads to a nonlinear system for which we get the local existence and uniqueness of a solution. We prove that \\S-f\\(infinity) = O(h(3)). Numerical test shows good approximation properties of these splines.